We study arc spaces and jet schemes of generic determinantal varieties. Using the natural
group action, we decompose the arc spaces into orbits, and analyze their structure. This …

An n× n nilpotent matrix B is determined up to conjugacy by a partition PB of n, its Jordan
type given by the sizes of its Jordan blocks. The Jordan type D (P) of a nilpotent matrix in the …

We characterize by pattern avoidance the Schubert varieties for GL n that are local complete
intersections (lci). For those Schubert varieties that are lci, we give an explicit minimal set of …

Motivated by using combinatorics to study jets of monomial ideals, we extend a definition of
jets from graphs to clutters. We offer some structural results on their vertex covers, and show …

In this thesis we consider the Grassmannian complex of projective configurations in weight 2
and 3, and Cathelineau's infinitesimal polylogarithmic complexes as well as a tangential …

This article concerns a problem in algebra that is completely elementary to state, yet, has
proven tantalizingly difficult and is as yet unsolved. Consider C [A, B, C], the C-subalgebra of …

JET SCHEMES OF THE COMMUTING MATRIX PAIRS SCHEME 1. Introduction Recall that
if F is an algebraically closed field, {xi,j, yi,j, Page 1 PROCEEDINGS OF THE AMERICAN …

In an earlier paper [T. Košir, BA Sethuraman, Determinantal varieties over truncated
polynomial rings, J. Pure Appl. Algebra 195 (2005) 75–95] we had begun a study of the …

In this thesis we study algebraic sets of tuples whose entries are mutually com-muting
matrices possibly satisfying some additional condition, such as nilpotence, or which satisfy …

We introduce a Macaulay2 package for working with jet schemes. The main method
constructs jets of ideals, polynomial rings and their quotients, ring homomorphisms, affine …